That feeling with your heart in your mouth as you know your going to hit but then just miss is no fun at all.
Had 1 of my car / bike accidents right near the area you are talking about in a traffic circle.
Was bombing down the hill on 1st towards Burrard and at the traffic circle on the corner of 1st and Arbutus a lady was coming down Arbutus. we both entered at the same time both at high speed. I almost squeaked through but her bumper clipped the edge of my rear wheel sending me over the bars flying through the air landing upside down on a construction sign skidding across the street.
It was both our faults and I walked away without a scratch.
I learned that day to never ever enter a traffic circle without slowing right down. If a car is headed in always assume they will go until they come to a complete stop and let you through.
Another real bad spot for traffic circle burners is Creelman Ave and Whyte Ave just off the Burrard st bridge towards the water. Something about the people living in that area and not giving a crap.